The objective of this thesis is the study and development of inverse finite element methods (IFEM) for the design of compliant mechanisms. The problem consists in determining the initial shape of a mechanism such that it attains the desired design shape under the effect of service loads. This is formally known as an inverse design problem in the literature. Compliant mechanisms are a special class of mechanisms that gain some of its motion by elastic deformation in one or more members, rather than from rigid-body translations and/or rotations of classical rigid-body mechanisms. Mechanisms synthesis deals with the design of a suitable mechanism for a specified task or performance, and it begins with a prescribed task that must be achieved by using a yet unknown sized or shaped mechanism.
It became evident that IFEM could make important contributions in the field of complaint mechanism design, in particular as a re-design tool, since IFEM solutions have shown better convergence than the direct methods from which they derive. It also avoids the trial and error approach used many times in the design process. This is novel methodology in the field of compliant mechanisms. There is no background of inverse methods among the procedures used to design compliant system since it departs from classical design methods used up-to-date, being so far the only design method that does not rely on the use of optimization techniques.